bettatantalo wrote:
Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?
a) 1 : 1
b) 2 : 1
c) 3 : 2
d) 13 : 27
e) 15 : 19
source gmat tutor
Beqa chose an excellent method. +1
We can also find amounts of each juice in a 4:1 mix, and set them in a ratio
To find concentration of, say, OJ in A,
sum the ratio parts.
Concentration = \(\frac{part}{total}=\frac{L}{L+OJ}\)
A mix: \(\frac{L}{OJ}=\frac{1}{3}\)
Total parts: (1 + 3) = 4
A, concentration of \(L = \frac{1}{4}\)
A, concentration of \(OJ=\frac{3}{4}\)
B mix: \(\frac{L}{OJ}=\frac{5}{3}\)
Total parts: (5 + 3) = 8
B, concentration of \(L = \frac{5}{8}\)
B, concentration of \(OJ=\frac{3}{8}\)
Drink A is mixed with drink B in the ratio of 4:1 to form drink C
So the amount of A in the resultant drink C is 4 times as much as B
Lemon juice only in 4A + 1B?
\((4)(\frac{1}{4})+(1)(\frac{5}{8})=\)
\((1+\frac{5}{8})=(\frac{8}{8}+\frac{5}{8})=\frac{13}{8}\)
Orange juice only in 4A+1B?
\((4)(\frac{3}{4})+(1)(\frac{3}{8})=\)
\((3+\frac{3}{8})=(\frac{24}{8}+\frac{3}{8})=\frac{27}{8}\)
Ratio of lemon juice to orange juice in C?
C = mix of 4A and 1B, as above
\(\frac{L}{OJ}=\frac{(\frac{13}{8})}{(\frac{27}{8})}=(\frac{13}{8}*\frac{8}{27})=\frac{13}{27}\)
Answer D
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